Articles and methods providing liquid-impregnated scale-phobic surfaces

ABSTRACT

This invention relates generally to articles, devices, and methods for inhibiting or preventing the formation of scale during various industrial processes. In certain embodiments, a vessel is provided for use in an industrial process, the vessel having a textured, liquid-impregnated surface in contact with a mineral solution, wherein the liquid-impregnated surface comprises a matrix of features spaced sufficiently close to stably contain an impregnating liquid lubricant therebetween or therewithin, wherein the impregnating lubricant has a low surface energy density, and wherein the spreading coefficient S os(w)  of the impregnating lubricant (subscript ‘o’) on the substrate (subscript ‘s’) in the presence of the salt solution (subscript ‘w’) is greater than zero, such that the impregnating lubricant fully submerges the textured substrate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and the benefit of U.S. ProvisionalPatent Application Ser. No. 61/922,574, filed Dec. 31, 2013, entitled“Articles and Methods Providing Liquid-Impregnated Scale-PhobicSurfaces,” and U.S. Provisional Patent Application Ser. No. 61/771,486,filed Mar. 1, 2013, entitled “Articles and Methods ProvidingLiquid-Impregnated Scale-Phobic Surfaces,” the disclosures of which areincorporated herein by reference in their entireties.

FIELD OF THE INVENTION

This invention relates generally to articles, devices, and methods forinhibiting or preventing the formation of scale on surfaces, and moreparticularly, to articles, devices, and methods for inhibiting orpreventing the formation of mineral scale on surfaces in industrialprocesses.

BACKGROUND OF THE INVENTION

Scale formation is a persistent problem encountered in a variety ofindustries, such as the oil and gas industry, desalination plants, andpower plants, among others, and results in a significant loss ofefficiency and useful lifetime of process equipment in these industries.For example, scale formation or precipitation fouling of heat exchangersurfaces and oil and gas pipelines are a significant problem. Developingsurfaces that have a low affinity to scale has been an area ofparticular interest in the last decade.

The challenges associated with scale formation have a major effect onthe capital and operating costs of most conversion processes. Forexample, the costs associated with heat exchanger fouling forindustrialized countries has been estimated to be about 0.25% of thegross national product (GNP) for these countries. Furthermore, scaleformation may play a dramatic role in oil pipelines. For example, scaleformation resulted in a shocking loss of production from 30,000barrels/day to 0 (zero) barrels/day in mere 24 hours in an oil well inthe North Sea, as discussed in Crabtree et al., Oilfield Rev. 1999,Autumn, 30.

Among well-known mineral scale deposits, CaSO₄ is a mineral scaledeposit encountered in many industrial processes. Besides having lowsolubility limits, a major difficulty with CaSO₄ is the phasetransformation between its hydrates and polymorphs, particularly atelevated temperatures (above 100° C.), which results in a significantreduction of its solubility limits. Furthermore, the solubility of CaSO₄is strongly affected by the presence and concentrations of other ions inthe system. Another challenge with CaSO₄ scale deposits is that theyform even at low pH and can be removed effectively only by mechanicalmeans, which significantly increases the operating cost of the plant.

Conventional techniques to remove scale deposits include mechanical andchemical methods. However, these techniques are suboptimal because ofthe high, often prohibitive, costs involved in the removal process, aswell as their environmentally unfriendly nature. For example,conventional methods for scale mitigation involving chemical additiveson surfaces can either shift the scale equilibrium conditions or act asinhibitors by increasing scale formation time. Other methods includecoating substrates with low surface energy materials to inhibit scaleformation. However, such chemical additives and coatings involvepolymers, thiols, or silanes, which can deteriorate under harshenvironments that are generally encountered during scale formation invarious industries, creating an environmental hazard.

Hence, to achieve further advances in economics and efficiency ofvarious processes, there is a need for innovative technologies for scalemitigation and control.

SUMMARY OF THE INVENTION

Presented herein are liquid-impregnated surfaces that combine thedesired properties of low surface energy and low roughness along with aliquid-liquid interface, all of which mitigates scale nucleation and/orgrowth on the surface. Furthermore, it is shown that standard vesselmaterials, such as steel (e.g., in some embodiments, the steel is carbonsteel or stainless steel), aluminum, copper, or tin, for example, can beinexpensively treated to produce a microtextured surface which issuitable for liquid impregnation. Moreover, an existing industrialvessel can be retrofitted by microtexturing its interior surface, thenimpregnating the microtextured surface with a low surface-energyimpregnating liquid.

Vessels (e.g., tanks or pipes) are presented herein that inhibit theformation of mineral scale deposits thereupon. The vessel has aliquid-impregnated interior surface, wherein the impregnating liquid isstably held within a matrix of micro- or nano-scale (solid) features onthe surface, or the impregnating liquid fills pores or other tiny wells(e.g., wells, cavities, hollows, recesses, pits, etc.) on the surface.The impregnating liquid is stably contained and does not leachsignificantly (or at all) into the contents of the vessel, even when thevessel contains another liquid, such as water. The impregnated lubricantis stabilized by capillary forces arising from the micro- or nano-scopictexture and can impart remarkable mobility to motive phase(s) (e.g.,liquid droplets) on the surface.

In certain embodiments, the vessel has a textured, liquid-impregnatedsurface in contact with a mineral solution, wherein the impregnatinglubricant has a low surface energy density, and wherein the spreadingcoefficient S_(os(w)) of the impregnating lubricant (subscript ‘o’) onthe substrate (subscript ‘s’) in the presence of the salt solution(subscript ‘w’) is greater than zero, such that the impregnatinglubricant fully submerges the textured substrate.

In one aspect, the present invention relates to a vessel for use in anindustrial process, the vessel comprising a liquid-impregnated interiorsurface, wherein the liquid-impregnated surface includes a matrix offeatures spaced sufficiently close to stably contain an impregnatingliquid therebetween or therewithin (e.g., to contain the impregnatingliquid sufficiently well such that small quantities of impregnatingliquid lost due to settling, evaporation, and/or dissolution of theimpregnating liquid into one or more other phases coming into contactwith the surface can be replenished, e.g., via contact with a reservoircontaining the impregnating liquid) and the impregnating liquid has asurface energy density γ (as measured at 25° C.) no greater than about35 mJ/m², (e.g., no greater than about 30 mJ/m², no greater than about25 mJ/m², or no greater than about 20 mJ/m²), thereby providingresistance to formation of mineral scale deposits thereupon (e.g., whenthe liquid-impregnated surface of the vessel is in contact with asolution comprising a scale-forming mineral) (e.g., wherein the vesselis designed for use in a process in which the liquid-impregnated surfaceof the vessel contains, transfers, or is otherwise in contact with asolution comprising a scale-forming mineral) (e.g., wherein theimpregnating liquid is immiscible with, or negligibly miscible with, thesolution comprising the scale-forming mineral with which the interiorsurface of the vessel is designed to come into contact).

In certain embodiments, the impregnating liquid is a lubricant and theinterior surface is a textured substrate, wherein the liquid-impregnatedinterior surface of the vessel is configured, during operation, to comeinto contact with (or maintain contact with) a salt solution comprisinga scale-forming mineral (e.g., wherein the vessel is designed for use ina process in which the liquid-impregnated surface of the vessel is incontact with a salt solution comprising a scale-forming mineral, orwherein the vessel contains a salt solution comprising a scale-formingmineral or transfers a salt solution comprising a scale-formingmineral), and wherein the spreading coefficient S_(os(w)) of theimpregnating lubricant (subscript ‘o’) on the substrate (subscript ‘s’)in the presence of the salt solution (subscript ‘w’) is greater thanzero, such that the impregnating lubricant fully submerges the texturedsubstrate (e.g., state IV in FIG. 1 d).

In certain embodiments, the impregnating liquid is a silicone oil. Incertain embodiments, the liquid-impregnated surface is a scale-phobicsurface that inhibits scale formation thereupon. In certain embodiments,the liquid-impregnated surface includes a (solid) metal. In certainembodiments, the metal is selected from the group consisting ofaluminum, steel (e.g., stainless or carbon steel), copper, titanium,tin, or any combinations thereof, alloys thereof, or oxides thereof.

In certain embodiments, the impregnating liquid submerges the surface.In certain embodiments, the liquid-impregnated surface includes a silanecoating. In certain embodiments, the silane coating is a member selectedfrom the group consisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane, andfluorosilane.

In certain embodiments, the liquid-impregnated surface is textured. Incertain embodiments, the liquid-impregnated surface includes micro-scaleand/or nano-scale features. In certain embodiments, the features includenanograss.

In certain embodiments, the liquid-impregnated surface is located on aninterior wall of a heat exchanger. In certain embodiments, the mineralscale deposits include at least one of calcium sulfate, calciumcarbonate, barium sulfate, silica, and/or iron.

In certain embodiments, the vessel is a conduit or receptacle (e.g.,pipeline) used in deep sea oil and/or gas recovery.

In certain embodiments, the vessel is a conduit or receptacle of a heatexchanger.

In another aspect, the present invention provides a method ofretrofitting a vessel for improved resistance to mineral scale deposits,the method comprising modifying the vessel to produce aliquid-impregnated surface, wherein the liquid-impregnated surfaceincludes a matrix of features spaced sufficiently close to stablycontain an impregnating liquid therebetween or therewithin (e.g., tocontain the impregnating liquid sufficiently well such that smallquantities of impregnating liquid lost due to settling, evaporation,and/or dissolution of the impregnating liquid into one or more otherphases coming into contact with the surface can be replenished, e.g.,via contact with a reservoir containing the impregnating liquid) and theimpregnating liquid has a surface energy density γ (as measured at 25°C.) no greater than about 35 mJ/m², (e.g., no greater than about 30mJ/m², no greater than about 25 mJ/m², or no greater than about 20mJ/m²), thereby providing resistance to mineral scale deposits thereupon(e.g., when the liquid-impregnated surface of the vessel is in contactwith a solution comprising a scale-forming mineral) (e.g., wherein thevessel is designed for use in a process in which the liquid-impregnatedsurface of the vessel contains, transfers, or is otherwise in contactwith a solution comprising a scale-forming mineral) (e.g., wherein theimpregnating liquid is immiscible with, or negligibly miscible with, thesolution comprising the scale-forming mineral with which the interiorsurface of the vessel is designed to come into contact).

In some embodiments, the impregnating liquid is a lubricant and theinterior surface is a textured substrate, wherein the liquid-impregnatedinterior surface of the vessel is configured, during operation, to comeinto contact with (or maintain contact with) a salt solution comprisinga scale-forming mineral (e.g., wherein the vessel is designed for use ina process in which the liquid-impregnated surface of the vessel is incontact with a salt solution comprising a scale-forming mineral, orwherein the vessel contains a salt solution comprising a scale-formingmineral or transfers a salt solution comprising a scale-formingmineral), and wherein the spreading coefficient S_(os(w)) of theimpregnating lubricant (subscript ‘o’) on the substrate (subscript ‘s’)in the presence of the salt solution (subscript ‘w’) is greater thanzero, such that the impregnating lubricant fully submerges the texturedsubstrate (e.g., state IV in FIG. 1 d).

In some embodiments, the impregnating liquid is a silicone oil. In someembodiments, the liquid-impregnated surface is a scale-phobic surfacethat inhibits scale formation thereupon. In some embodiments, theliquid-impregnated surface includes a (solid) metal. In someembodiments, the metal is selected from the group consisting ofaluminum, steel (e.g., stainless or carbon steel), copper, titanium,tin, or any combinations thereof, alloys thereof, or oxides thereof. Insome embodiments, the impregnating liquid submerges the surface. In someembodiments, the liquid-impregnated surface includes a silane coating.In some embodiments, the silane coating is a member selected from thegroup consisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane, andfluorosilane, or any combination thereof.

In some embodiments, the liquid-impregnated surface is textured. In someembodiments, the liquid-impregnated surface includes micro-scale and/ornano-scale features. In some embodiments, the features includenanograss.

In some embodiments, the liquid-impregnated surface is located on aninterior wall of a heat exchanger. In some embodiments, the mineralscale deposits include at least one of calcium sulfate, calciumcarbonate, barium sulfate, silica, and/or iron.

In some embodiments, the vessel is a conduit or receptacle (e.g.,pipeline or part of a pipeline) used in deep sea oil and/or gasrecovery. In some embodiments, the vessel is a conduit or receptacle ofa heat exchanger.

In another aspect, the invention provides a method of using a vessel inan industrial process, the method comprising: (a) providing a vesselcomprising a liquid-impregnated surface, wherein the liquid-impregnatedsurface includes a matrix of features spaced sufficiently close tostably contain an impregnating liquid therebetween or therewithin (e.g.,to contain the impregnating liquid sufficiently well such that smallquantities of impregnating liquid lost due to settling, evaporation,and/or dissolution of the impregnating liquid into one or more otherphases coming into contact with the surface can be replenished, e.g.,via contact with a reservoir containing the impregnating liquid) and theimpregnating liquid has a surface energy density γ (as measured at 25°C.) no greater than about 35 mJ/m², (e.g., no greater than about 30mJ/m², no greater than about 25 mJ/m², or no greater than about 20mJ/m²), thereby providing resistance to mineral scale deposits thereupon(e.g., when the liquid-impregnated surface of the vessel is in contactwith a solution comprising a scale-forming mineral); and (b) contactingthe liquid-impregnated surface with a solution comprising ascale-forming mineral (e.g., wherein the impregnating liquid isimmiscible with, or negligibly miscible with, the solution comprisingthe scale-forming mineral with which the interior surface of the vesselis designed to come into contact).

In some embodiments, the method includes contacting theliquid-impregnated surface with a reservoir containing the impregnatingliquid to replenish any impregnating liquid lost due to settling,evaporation, and/or dissolution into one or more other phases cominginto contact with the liquid-impregnated surface.

In some embodiments, the impregnating liquid is a lubricant and theinterior surface is a textured substrate, wherein the liquid-impregnatedinterior surface of the vessel is configured, during operation, to comeinto contact with (or maintain contact with) a salt solution comprisinga scale-forming mineral (e.g., wherein the vessel is designed for use ina process in which the liquid-impregnated surface of the vessel is incontact with a salt solution comprising a scale-forming mineral, orwherein the vessel contains a salt solution comprising a scale-formingmineral or transfers a salt solution comprising a scale-formingmineral), and wherein the spreading coefficient S_(os(w)) of theimpregnating lubricant (subscript ‘o’) on the substrate (subscript ‘s’)in the presence of the salt solution (subscript ‘w’) is greater thanzero, such that the impregnating lubricant fully submerges the texturedsubstrate (e.g., state IV in FIG. 1 d).

In some embodiments, the impregnating liquid is a silicone oil. In someembodiments, the liquid-impregnated surface is a scale-phobic surfacethat inhibits scale formation thereupon. In some embodiments, theliquid-impregnated surface includes a (solid) metal. In someembodiments, the metal is selected from the group consisting ofaluminum, steel (e.g., stainless or carbon steel), copper, titanium,tin, or any combinations thereof, alloys thereof, or oxides thereof. Insome embodiments, the impregnating liquid submerges the surface.

In some embodiments, the liquid-impregnated surface includes a silanecoating. In some embodiments, the silane coating is a member selectedfrom the group consisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane,fluorosilane, or any combination thereof.

In some embodiments, the liquid-impregnated surface is textured. In someembodiments, the liquid-impregnated surface includes micro-scale and/ornano-scale features. In some embodiments, the features includenanograss.

In some embodiments, the liquid-impregnated surface is located on aninterior wall of a heat exchanger. In some embodiments, the mineralscale deposits include at least one of calcium sulfate, calciumcarbonate, barium sulfate, silica, and/or iron, or any combinationthereof.

In some embodiments, the vessel is a conduit or receptacle (e.g.,pipeline or part of a pipeline) used in deep sea oil and/or gasrecovery. In some embodiments, the vessel is a conduit or receptacle ofa heat exchanger (or a portion thereof).

In alternative embodiments of the vessels and methods described herein,the impregnating ‘liquid’ is not a liquid, but rather, is a gel, asemi-solid, or a low surface-energy solid (e.g., a gel, a semi-solid, ora low surface-energy solid with a surface energy density that is similarto that of a liquid).

Elements of embodiments described with respect to a given aspect of theinvention may be used in various embodiments of another aspect of theinvention. For example, it is contemplated that features of dependentclaim depending from one independent claim can be used in apparatus,articles, systems, and/or methods of any of the other independentclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the invention can be better understood withreference to the drawings described below, and the claims. The drawingsare not necessarily to scale, emphasis instead generally being placedupon illustrating the principles of the invention. In the drawings, likenumerals are used to indicate like parts throughout the various views.

While the invention is particularly shown and described herein withreference to specific examples and specific embodiments, it should beunderstood by those skilled in the art that various changes in form anddetail may be made therein without departing from the spirit and scopeof the invention.

FIG. 1 a is a schematic cross-sectional view of a liquid contacting anon-wetting surface, in accordance with certain embodiments of theinvention.

FIG. 1 b is a schematic cross-sectional view of a liquid that hasimpaled a non-wetting surface, in accordance with certain embodiments ofthe invention.

FIG. 1 c is a schematic cross-sectional view of a primary liquid incontact with a liquid-impregnated surface, in accordance with certainembodiments of the invention.

FIG. 1 d is a regime map showing four different states of alubricant-impregnated surface with a high surface tension and a lowsurface tension lubricant, in accordance with certain embodiments of theinvention.

FIG. 1 e illustrates a schematic diagram of a liquid droplet placed on atextured surface impregnated with a lubricant that wets the solidcompletely.

FIG. 1 f illustrates a schematic diagram of a liquid droplet placed on atextured surface impregnated with a lubricant that wets the solid with anon-zero contact angle in the presence of air and the droplet liquid.

FIG. 1 g illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with silicone oil.

FIG. 1 h illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm).

FIGS. 1 i and 1 j illustrate a water droplet under UV illumination whena fluorescent dye was dissolved in silicone oil and BMIm. The bottomregions show that the lubricating oils are pulled up above the texturesurface (b=50 μm).

FIGS. 1 k and 1 l show laser confocal fluorescence microscopy (LCFM)images of the impregnated texture showing that post tops were bright inthe case of silicone oil (FIG. 1 k), suggesting that they were coveredwith oil, and were dark in the case of BMIm (FIG. 1 l), suggesting thatthey were dry.

FIG. 1 m illustrates an ESEM image of the impregnated texture showingthe silicone oil trapped in the texture and suggesting that the filmthat wets the post tops is thin.

FIG. 1 n illustrates a SEM image of the texture impregnated with BMImshowing discrete droplets on post tops indicating that a film was notstable in this case.

FIG. 1 o illustrates schematics of wetting configurations outside andunderneath a drop. The total interface energies per unit area arecalculated for each configuration by summing the individual interfacialenergy contributions. Equivalent requirements for stability of eachconfiguration are also shown in FIG. 1 e.

FIG. 1 p illustrates a schematic diagram of possible thermodynamicstates of a water droplet placed on a lubricant-encapsulated surface.The top two schematics illustrate whether or not the droplet becomescloaked by the lubricant. For each case, there are six possible states,as illustrated, depending on how the lubricant wets the texture in thepresence of air (the vertical axis) and water (horizontal axis).

FIG. 1 q is a schematic describing six liquid-impregnated surfacewetting states, in accordance with certain embodiments of the invention.

FIG. 2 shows a comparison of the calcium sulfate salt formation on (a)smooth silicon and (b) a liquid-impregnated surface, in accordance withcertain embodiments of the invention.

FIG. 3 illustrates a schematic cross-sectional and corresponding topview of a liquid-impregnated surface that is partially submerged.

FIG. 4 shows a schematic illustration of the experimental set-up used inthe Examples.

FIG. 5 are SEMs showing results from Example 1, illustrating the effectof the impregnating liquid on scale formation. The figure shows theschematics of the liquid-impregnated surfaces and the images of the twosamples after scaling experiments performed with different liquids.

FIG. 6 shows two graphs of experimental results showing mass gain onvarious substrates due to scale formation.

FIG. 7 a shows an example experimental set-up used in the Examples inaccordance with some embodiments of the invention.

FIG. 7 b shows surface coverage of an untreated silicon and silicone oilimpregnated silicon at different times.

FIG. 7 c shows a series of photographs illustrating scale formation onbare silicon substrate after 33, 53, and 80 hours, respectively. Thescale bar in FIG. 7 c is 1 mm.

FIG. 7 d shows a series of photographs illustrating scale formation onsilicone oil-impregnated substrates after 33, 53, and 80 hours,respectively. The scale bar in FIG. 7 d is 1 mm. These photographsdemonstrate delay in scale incubation time on the liquid-impregnatedsurface, according to some embodiments of the invention.

FIG. 8 a illustrates a schematic of lubricant impregnation in steel,according to some embodiments of the present invention.

FIG. 8 b is an SEM image of a sandblasted steel substrate; the scale baris 50 μm.

FIGS. 8 c and 8 d are photographs of (c) bare steel and (d) impregnatedsteel before washing with a steady stream of water at a flow rate ofabout 150 ml/min for ˜30 seconds. The scale bar is 5 mm.

FIGS. 8 e and 8 f are SEM images of (e) bare steel and (f) impregnatedsteel before washing with a steady stream of water at a flow rate ofabout 150 ml/min for ˜30 seconds. The scale bar is 1 mm.

FIGS. 8 g and 8 h are photographs of (g) bare steel and (h) impregnatedsteel after washing with a steady stream of water at a flow rate ofabout 150 ml/min for ˜30 seconds. The scale bar is 5 mm.

FIGS. 8 i and 8 j are SEM images of (i) bare steel and (j) impregnatedsteel after washing with a steady stream of water at a flow rate ofabout 150 ml/min for ˜30 seconds. The scale bar is 1 mm.

Also shown is a comparison of the scale-inhibiting performance of smoothstainless steel compared with liquid-impregnated stainless steel.

FIG. 9 shows a comparison of the corrosion on two substrates (left) barecarbon steel and (right) liquid impregnated carbon steel, according toan illustrative embodiment of the invention.

FIGS. 10 a-b illustrate schematics of a smooth uncoated siliconsubstrate and a lubricant-impregnated nano-textured silicon substrate,respectively, according to some embodiments of the invention.

FIGS. 10 c-d illustrate photographs of calcium sulfate (CaSO₄) scaleformation after ˜80 hours of residence time on a smooth uncoated siliconsubstrate and a lubricant-impregnated nano-textured silicon substrate,respectively. The scale bar in FIGS. 10 c-d is 5 mm.

FIGS. 10 e-f illustrate SEM images of CaSO₄ scale formation after ˜80hours of residence time on a smooth uncoated silicon substrate and alubricant-impregnated nano-textured silicon substrate, respectively. Thescale bar in FIGS. 10 e-f is 1 mm.

DETAILED DESCRIPTION

It is contemplated that compositions, mixtures, systems, devices,methods, and processes of the claimed invention encompass variations andadaptations developed using information from the embodiments describedherein. Adaptation and/or modification of the compositions, mixtures,systems, devices, methods, and processes described herein may beperformed by those of ordinary skill in the relevant art.

Throughout the description, where articles, devices and systems aredescribed as having, including, or comprising specific components, orwhere processes and methods are described as having, including, orcomprising specific steps, it is contemplated that, additionally, thereare articles, devices, and systems of the present invention that consistessentially of, or consist of, the recited components, and that thereare processes and methods according to the present invention thatconsist essentially of, or consist of, the recited processing steps.

Similarly, where articles, devices, mixtures, and compositions aredescribed as having, including, or comprising specific compounds and/ormaterials, it is contemplated that, additionally, there are articles,devices, mixtures, and compositions of the present invention thatconsist essentially of, or consist of, the recited compounds and/ormaterials.

It should be understood that the order of steps or order for performingcertain actions is immaterial so long as the invention remains operable.Moreover, two or more steps or actions may be conducted simultaneously.

The mention herein of any publication, for example, in the Backgroundsection, is not an admission that the publication serves as prior artwith respect to any of the claims presented herein. The Backgroundsection is presented for purposes of clarity and is not meant as adescription of prior art with respect to any claim.

Described herein are embodiments and experiments with liquid-impregnatedsubstrates with varying surface energies for which a demonstration ofthe effect of surface energy on scale formation is performed. Scaleformation can be qualitatively (using SEM) and quantitatively (weightgain) observed at various residence times, in contact with a mineralsolution.

Without wishing to be bound by any theory, it is believed that saltparticles nucleate on surfaces at a rate given by

$\begin{matrix}{J = {N\; \beta^{*}\exp^{- \frac{\Delta \; G^{*}}{k_{B}T}}}} & (1)\end{matrix}$

The activation barrier (ΔG*) required for this nucleation dictates therate at which the salt nucleates. Another factor that plays a role indetermining the rate of nucleation is the number of potential nucleationsites (N) available for these salt particles. Without wishing to bebound by a particular theory, an extremely smooth surface with a verylow surface energy would be a preferable surface to combat scalingproblems. Mechanical damage may lead to increased roughness therebyreducing the effectiveness of these surfaces.

The precipitation of scale is believed to follow the nucleation-growthmechanism. The steady-state nucleation rate J at a temperature T isgiven by the classical nucleation theory Equation (2) below

$\begin{matrix}{J = {{NZ}\; \beta^{*}\exp^{- \frac{\Delta \; G^{*}}{k_{B}T}}}} & (2)\end{matrix}$

where N is the density of nucleation sites, β* is the atomic attachmentrate, Z is the Zeldovich's factor, and (ΔG*) is the activation barrierfor nucleation. The density of nucleation sites N, depends on theroughness and heterogeneity of the surface, with a smoother surfacecorresponding to a lower nucleation site density and hence lowernucleation rate. The activation barrier for nucleation, ΔG*, depends onthe surface properties and is given by the Equation (3) below

$\begin{matrix}{{\Delta \; G^{*}} = {\frac{\pi \; \sigma_{cw}r^{*^{2}}}{3}\left( {2 - {3m} + m^{3}} \right)}} & (3)\end{matrix}$

where σ_(cw) is the salt nucleus (c)−salt solution (w) interfacialenergy, r* is the critical size of the nucleus, m is the ratio of theinterfacial energies given by Equation (4) below:

$\begin{matrix}{m = \frac{\sigma_{sw} - \sigma_{cs}}{\sigma_{cw}}} & (4)\end{matrix}$

where σ_(sw) and σ_(cs) are the interfacial energies of [the substrate(s)−salt solution (w)] and [the substrate (s)−salt nucleus (c)interfaces], respectively. The activation barrier ΔG* is high on lowenergy surfaces. In some embodiments, a smooth, low energy surface isideal to combat scale problems.

The thermodynamic state of a lubricant-impregnated surface depends onthe choice of the lubricant and the geometry of the underlying texture.Having a stable impregnated state is important to avoid the displacementof the lubricant by the salt solution. The value of Θ_(c) is calculatedusing the Equation (5) below:

$\begin{matrix}{\Theta_{c} = {\cos^{- 1}\left( \frac{1 - \varphi}{r - \varphi} \right)}} & (5)\end{matrix}$

In Eq. (5), φ is the solid fraction of the projected area of a texturedsurface and r is the roughness of the substrate given by the ratio ofthe total surface area to the projected surface area. An extremely roughtextured solid (e.g., large r) is preferred in some embodiments as theunderlying substrate for lubricant-impregnated surface to maintain astable impregnating state.

FIG. 1 d illustrates a regime map of the stable states oflubricant-impregnated surface immersed in salt solution. Four differentstates (I, II, III, and IV) are possible based on the properties of theimpregnating lubricant—surface tension (σ) and the spreading coefficient(S_(os(w))). The spreading coefficient of the lubricant (subscript ‘o’)on the substrate (subscript ‘s’) in the presence of the salt solution(subscript ‘w’) is given by Equation (6) below:

S _(os(w))=σ_(sw)−σ_(os)−σ_(ow)  (6)

where σ_(sw), σ_(os), and σ_(ow) are the interfacial energies ofsubstrate-salt solution, lubricant-substrate, and lubricant-saltsolution, respectively.

Depending on the surface tension of the lubricant, the substrate caneffectively have a high-energy surface (states I and III in FIG. 1 d) ora low-energy surface (states II and IV in FIG. 1 d). This factorinfluences the activation barrier for nucleation on thelubricant-impregnated surface: an impregnating lubricant with a lowsurface tension results in a high activation barrier (ΔG*) fornucleation on the surface and vice versa.

Furthermore, the impregnating lubricant controls the density ofnucleation sites (N) depending on its spreading coefficient on thesurface in the presence of salt solution: an impregnating lubricant witha positive spreading coefficient submerges the entire texture (statesIII and IV in FIG. 1 d), while a lubricant with a negative spreadingcoefficient would result in the tops of the texture being exposed to thesalt solution (states I and II in FIG. 1 d). An impregnated surface withsubmerged texture has a much lower density of nucleation sites (N)compared to an impregnated surface with the texture tops exposed to thesalt solution. Thus, with an optimized design of the lubricant (which insome embodiments refers to low N and high (ΔG*), thelubricant-impregnated surface can satisfy the criteria for effectivescale-resistant surfaces (state IV in FIG. 1 d).

It is found herein that liquid-impregnated surfaces that combine theproperties of low surface energy and high degree of smoothness alongwith high resistance to mechanical damage because of the self-healingproperty of these surfaces exhibit desirable scale resistanceproperties.

Liquid impregnated interfaces may include a low surface energy texturedsolid for capillary stabilization and a suitable impregnating liquidhaving a low polar component of surface energy. In some embodiments, theimpregnating liquid submerges the entire texture. In some embodiments,the impregnating liquid only partially submerges the texture.

In some embodiments of liquid-impregnated surfaces described herein,emerged area fraction φ is less than 0.30, 0.25, 0.20, 0.15, 0.10, 0.05,0.01, or 0.005. In some embodiments, φ is greater than 0.001, 0.005,0.01, 0.05, 0.10, 0.15, or 0.20. In some embodiments, φ is in a range ofabout 0 and about 0.25. In some embodiments, φ is in a range of about 0and about 0.01. In some embodiments, φ is in a range of about 0.001 andabout 0.25. In some embodiments, φ is in a range of about 0.001 andabout 0.10.

In some embodiments, the liquid-impregnated surface is configured suchthat cloaking by the impregnating liquid can be either eliminated orinduced, according to different embodiments described herein.

As used herein, the spreading coefficient, S_(ow(a)) is defined asγ_(wa)−γ_(wo)−γ_(oa), where γ is the interfacial tension between the twophases designated by subscripts w, a, and o, where w is water, a is air,and o is the impregnating liquid. Interfacial tension can be measuredusing a pendant drop method as described in Stauffer, C. E., “Themeasurement of surface tension by the pendant drop technique,” J. Phys.Chem. 1965, 69, 1933-1938, the text of which is incorporated byreference herein. Exemplary surfaces and its interfacial tensionmeasurements (at approximately 25° C.) are Table 3 below.

Without wishing to be bound to any particular theory, impregnatingliquids that have S_(ow(a)) less than 0 will not cloak matter as seen inFIG. 1 g, resulting in no loss of impregnating liquids, whereasimpregnating liquids that have S_(ow(a)) greater than 0 will cloakmatter (condensed water droplets, bacterial colonies, solid surface) asseen in FIG. 1 f and this may be exploited to prevent corrosion,fouling, etc. In certain embodiments, cloaking is used for preventingvapor-liquid transformation (e.g., water vapor, metallic vapor, etc.).In certain embodiments, cloaking is used for inhibiting liquid-solidformation (e.g., ice, metal, etc.). In certain embodiments, cloaking isused to make reservoirs for carrying the materials, such thatindependent cloaked materials can be controlled and directed by externalmeans (like electric or magnetic fields).

FIG. 1 g illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with silicone oil. FIG. 1 hillustrates a water droplet on a silicon micro post surface (post sidea=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm).FIGS. 1 i and 1 j illustrate a water droplet under UV illumination whena fluorescent dye was dissolved in silicone oil and BMIm. The bottomregions show that the lubricating oils are pulled up above the texturesurface (b=50 μm).

FIG. 1 g shows an 8 μl water droplet placed on the silicone oilimpregnated texture. The droplet forms a large apparent contactangle)(˜100° but very close to the solid surface (shown by arrows inFIG. 1 g), its profile changes from convex to concave.

When a fluorescent dye was added to the silicone oil and imaged under UVlight, the point of inflection corresponded to the height to which anannular ridge of oil was pulled up in order to satisfy a vertical forcebalance of the interfacial tensions at the inflection point (FIG. 10.Although the oil should spread over the entire droplet (FIG. 1 g), thecloaking film was too thin to be captured in these images. The “wettingridge” was also observed in the case of ionic liquid (FIGS. 1 h, 1 j).The importance of the wetting ridge to droplet mobility will bediscussed below. Such wetting ridges are reminiscent of those observedaround droplets on soft substrates.

The texture can be completely submerged in the oil if θ_(os(a))=0°. Thiscondition was found to be true for silicone oil, implying that the topsof the posts should be covered by a stable thin oil film. This film wasobserved experimentally using laser confocal fluorescence microscopy(LCFM); the post tops appear bright due to the presence of a fluorescentdye that was dissolved in the oil (FIG. 1 k). Environmental SEM imagesof the surface (FIG. 1 m) show the oil-filled texture and confirm thatthis film is less than a few microns thick, consistent with priorestimates of completely-wetting films. On the other hand, BMIm has anon-zero contact angle on a smooth OTS-coated silicon surface(θ_(os(a))=65±5°) indicating that with this lubricant the post topsshould remain dry. Indeed, LCFM images confirmed this (FIG. 1 (h))—thepost tops appear dark as there is no dye present to fluoresce. SinceBMIm is conductive and has an extremely low vapor pressure, it could beimaged in a SEM. As shown in FIG. 1 n, discrete droplets resting on posttops are seen, confirming that a thin film was not stable on the posttops in this case.

The stable wetting configuration affects the mobility of droplets. Asshown in FIG. 1 f, in the case of BMIm, there are three distinct phasecontact lines at the perimeter of the drop that confine the wettingridge: the oil-water-air contact line, the oil-solid-air contact lineoutside the drop, and the oil-solid-water contact line underneath thedrop. These contact lines exist because θ_(os(a))>0, _(θos(w))>0, andS_(ow(a))<0. In contrast, in the case of silicone oil (FIG. 1 e), noneof these contact lines exist because θ_(os(a))=0, θ_(os(w))=0, andS_(ow(a))>0. These configurations are just two of the 12 differentconfigurations in such a four-phase system where oil impregnation ispossible. These configurations are discussed below.

A thermodynamic framework that allows one to predict which of these 12states will be stable for a given droplet, oil, and substrate materialwill be discussed in the paragraphs below. There are three possibleconfigurations to consider for the interface outside of the droplet (inan air environment), and three possible configurations to consider forthe interface underneath the droplet (in a water environment). Theseconfigurations are shown in FIG. 1 o along with the total interfaceenergy of each configuration. The configurations possible outside thedroplet are A1 (not impregnated, i.e., dry), A2 (impregnated withemergent features), and A3 (impregnated with submerged features—i.e.,encapsulated). On the other hand, underneath the droplet, the possibleconfigurations are W1 (impaled), W2 (impregnated with emergentfeatures), and W3 (impregnated with submerged features—i.e.,encapsulated). The stable configuration will be the one that has thelowest total interface energy. Referring now to configurations outsidethe droplet, the textured surface as it is slowly withdrawn from areservoir of oil could be in any of states A1, A2, and A3 depending onwhich has the lowest energy. For example, state A2 would be stable if ithas the lowest total interface energy, i.e. E_(A2)<E_(A1), E_(A3). FromFIG. 1 o, this results in:

E _(A2) <E _(A1)

(γ_(sa)−γ_(os))/γ_(oa)>(1−φ)/(r−φ)  (7)

E _(A2) <E _(A3)

γ_(sa)−γ_(os)−γ_(oa)<0  (8)

where φ is the fraction of the projected area of the surface that isoccupied by the solid and r is the ratio of total surface area to theprojected area of the solid. In the case of square posts with width “a”,edge-to-edge spacing “b”, and height “h”, φ=a²/(a+b)² andr=1+4ah/(a+b)². Applying Young's equation,cos(θos(a))=(γ_(sa)−γ_(os))/γ_(oa), Eq. (7) reduces to the hemi-wickingcriterion for the propagation of oil through a textured surface:cos(θ_(oa(a)))>(1−φ)/(r−φ)=cos(θ_(c)). This requirement can beconveniently expressed as θ_(os(a))<θ_(c). In Eq. (8),γ_(sa)−γ_(os)−γ_(oa), is simply the spreading coefficient S_(os(a)) ofoil on the textured surface in the presence of air. This may bereorganized as (γ_(sa)−γ_(os))/γ_(oa)<1, and applying Young's equationagain, Eq. (8) can be written as θ_(os(a))>0. Expressing Eq. (7) interms of the spreading coefficient S_(os(a)), yields:−γ_(oa)(r−1)/(r−φ)<S_(os(a)). The above simplifications then lead to thefollowing equivalent criteria for the surface to be in state A2:

E _(A2) <E _(A1) ,E _(A3)

θ_(c)>θ_(os(a))>0

−γ_(oa)(r−1)/(r−φ)<S _(os(a))<0  (9)

Similarly, state A3 would be stable if E_(A3)<E_(A2), E_(A1). From FIG.1 o, this gives:

E _(A3) <E _(A2)

θ_(os(a))=0

γ_(sa)−γ_(os)−γ_(oa) ≡S _(os(a))≧0  (10)

E _(A3) <E _(A1)

θ_(os(a))<cos⁻¹(1/r)

S_(os(a))>γ_(oa)(1/1/r)  (11)

Note that Eq. (11) is automatically satisfied by Eq. (10), thus thecriterion for state A3 to be stable (i.e., encapsulation) is given byEq. (10). Following a similar procedure, the condition for state A1 tobe stable can be derived as

E _(A1) <E _(A2) ,E _(A3)

θ_(os(a))>θ_(c)

S_(os(a))<−γ_(oa)(r−1)/(r−φ)  (12)

The rightmost expression of Eq. (10) can be rewritten as(γ_(sa)−γ_(os))/γ_(oa)>1. This raises an important point: Young'sequation would suggest that if θ_(os(a))=0, then(γ_(sa)−γ_(os))/γ_(oa)=1 (i.e., S_(os(a))=0). However, θ_(os(a))=0 istrue also for the case that (γ_(sa)−γ_(os))/(γ_(oa)>1 (i.e.S_(os(a))>0). It is important to realize that Young's equation predictsthe contact angle based on balancing the surface tension forces on acontact line—the equality only exists for a contact line at staticequilibrium. For a spreading film (S_(os(a))>0) a static contact linedoesn't exist, hence precluding the applicability of Young's equation.

The configurations possible underneath the droplet are discussed in theparagraphs below. Upon contact with water, the interface beneath thedroplet will attain one of the three different states—W1, W2, or W3(FIG. 1 o)—depending on which has the lowest energy. Applying the samemethod to determine the stable configurations of the interface beneaththe droplet, and using the total interface energies provided in Table 1,the stability requirements take a form similar to Eqs. (9), (10), and(12), with γ_(oa), γ_(sa), θ_(os(a)), S_(os(a)), replaced with γ_(ow),γ_(sw), θ_(os(w)), S_(os(w)), respectively. In some embodiments, θ_(c)is not affected by the surrounding environment as it is only a functionof the texture parameters, φ and r. Thus, the texture will remainimpregnated with oil beneath the droplet with emergent post tops (i.e.,state W2) when:

E _(W2) <E _(W1) ,E _(W3)

θ_(c)>θ_(os(w))>0

−γ_(ow)(r−1)/(r−φ)<S _(os(w))<0  (13)

State W3 will be stable (i.e., the oil will encapsulate the texture)when:

E _(W3) <E _(W1) ,E _(W2)

θ_(os(w))=0

γ_(sw)−γ_(os)−γ_(ow) ≡S _(os(w))≧0  (14)

and the droplet will displace the oil and be impaled by the textures(state W1) when:

E _(W1) <E _(W2) ,E _(W3)

θ_(os(w))>θ_(c)

S _(os(w))<−γ_(ow)(r−1)/(r−φ)  (15)

Combining the above criteria along with the criterion for cloaking ofthe water droplet by the oil film, the various possible states can beorganized in a regime map, which is shown FIG. 1 p. The cloakingcriterion is represented by the upper two schematic drawings. For eachof these cases, there are six different configurations possibledepending on how the oil interacts with the surface texture in thepresence of air (vertical axis in FIG. 1 p) and water (horizontal axisin FIG. 1 p). The vertical and horizontal axes are the normalizedspreading coefficients S_(os(a))/γ_(oa) and S_(os(w))/γ_(ow)respectively. Considering first the vertical axis of FIG. 1 p, whenS_(os(a))/γ_(oa)<−(r−1)/(r−φ), i.e., when Eq. (12) holds, oil does noteven impregnate the texture. As S_(os(a))/γ_(oa) increases above thisimportant value, impregnation becomes feasible but the post tops arestill left emerged. Once S_(os(a))/γ_(oa)>0, the post tops are alsosubmerged in the oil leading to complete encapsulation of the texture.Similarly, on the x-axis of FIG. 1 p moving from left to right, asS_(os(w))/γ_(ow) increases, the droplet transitions from an impaledstate to an impregnated state to a fully-encapsulated state. Althoughprior studies have proposed simple criteria for whether a deposited dropwould float or sink, additional states, as shown in FIG. 1 p, were notrecognized.

FIG. 1 p shows that there can be up to three different contact lines,two of which can get pinned on the texture. The degree of pinningdetermines the roll-off angle α*, the angle of inclination at which adroplet placed on the textured solid begins to move. Droplets thatcompletely displace the oil (states A3-W1, A2-W1 in FIG. 1 p) are notexpected to roll off the surface. These states are achieved whenθ_(os(w))>θ_(c), as is the case for both BMIm and silicone oilimpregnated surfaces when the silicon substrates are not treated withOTS. As expected, droplets did not roll off of these surfaces. Dropletsin states with emergent post tops (A3-W2, A2-W2, A2-W3) are expected tohave reduced mobility that is strongly texture dependent, whereas thosein states with encapsulated posts outside and beneath the droplet (theA3-W3 states in FIG. 1 p) are expected to exhibit no pinning andconsequently infinitesimally small roll-off angles.

Droplets placed on lubricant-impregnated surfaces exhibit fundamentallydifferent behavior compared to typical superhydrophobic surfaces. Insome embodiments, these four-phase systems can have up to threedifferent three-phase contact lines, giving up to twelve differentthermodynamic configurations. In some embodiments, the lubricant filmencapsulating the texture is stable only if it wets the texturecompletely (θ=0), otherwise portions of the textures dewet and emergefrom the lubricant film. In some embodiments, complete encapsulation ofthe texture is desirable in order to eliminate pinning. In someembodiments, texture geometry and hierarchical features can be exploitedto reduce the emergent areas and achieve roll-off angles close to thoseobtained with fully wetting lubricants. In some embodiments, droplets oflow-viscosity liquids, such as water placed on these impregnatedsurfaces, roll rather than slip with velocities that vary inversely withlubricant viscosity. In some embodiments, additional parameters, such asdroplet and texture size, as well as the substrate tilt angle, may bemodeled to achieve desired droplet (and/or other substance) movement(e.g., rolling) properties and/or to deliver optimal non-wettingproperties.

FIG. 1 q is a schematic describing six liquid-impregnated surfacewetting states, in accordance with certain embodiments described herein.The six surface wetting states (state 1 through state 6) depend on thefour wetting conditions shown at the bottom of FIG. 1 q (conditions 1 to4). In some embodiments, the non-wetted states are preferred (states 1to 4). Additionally, where a thin film stably forms on the tops of theposts (or other features on the surface), as in non-wetted states 1 and3, even more preferable non-wetting properties (and other relatedproperties described herein) may be observed.

In order to achieve non-wetted states, it is often preferable to havelow solid surface energy and low surface energy of the impregnatedliquid compared to the nonwetted liquid. For example, surface energiesbelow about 25 mJ/m² are desired in some embodiments. Low surface energyliquids include certain hydrocarbon and fluorocarbon-based liquids, forexample, silicone oil, perfluorocarbon liquids, perfluorinated vacuumoils (e.g., Krytox 1506 or Fromblin 06/6), fluorinated coolants such asperfluoro-tripentylamine (e.g., FC-70, sold by 3M, or FC-43),fluorinated ionic liquids that are immiscible with water, silicone oilscomprising PDMS, and fluorinated silicone oils.

Examples of low surface energy solids include the following: silanesterminating in a hydrocarbon chain (such as octadecyltrichlorosilane),silanes terminating in a fluorocarbon chain (e.g., fluorosilane), thiolsterminating in a hydrocarbon chain (such butanethiol), and thiolsterminating in a fluorocarbon chain (e.g. perfluorodecane thiol). Incertain embodiments, the surface includes a low surface energy solidsuch as a fluoropolymer, for example, a silsesquioxane such asfluorodecyl polyhedral oligomeric silsesquioxane. In certainembodiments, the fluoropolymer is (or includes) tetrafluoroethylene(ETFE), fluorinated ethylenepropylene copolymer (FEP), polyvinylidenefluoride (PVDF), perfluoroalkoxytetrafluoroethylene copolymer (PFA),polytetrafluoroethylene (PTFE), tetrafluoroethylene,perfluoromethylvinylether copolymer (MFA),ethylenechlorotrifluoroethylene copolymer (ECTFE),ethylene-tetrafluoroethylene copolymer (ETFE), perfluoropolyether,and/or Tecnoflon.

In certain embodiments, an impregnating liquid is or includes an ionicliquid. Ionic liquids have extremely low vapor pressures (˜10⁻¹² mmHg),and therefore they mitigate the concern of the lubricant loss throughevaporation. In some embodiments, an impregnating liquid can be selectedto have a S_(ow(a)) less than 0. Exemplary impregnating liquids include,but are not limited to, tetrachloroethylene (perchloroethylene), phenylisothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene,o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene,acetylene tetrabromide, 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl) imide (BMIm), tribromohydrin(1,2,3-tribromopropane), tetradecane, cyclohexane, ethylene dibromide,carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax,Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene,perchloroethylene, carbon disulfide, phenyl mustard oil,monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide,aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleicacid, linoleic acid, amyl phthalate and any combination thereof.

In accordance with some embodiments of the present invention, exemplarysolid features include, but are not limited to, polymeric solid, aceramic solid, a fluorinated solid, an intermetallic solid, and acomposite solid and any combination thereof. As demonstrated in FIG. 3,solid features can include any suitable shapes and/or define anysuitable structures. Exemplary solid features include, but are notlimited to, pores, cavities, wells, interconnected pores, andinterconnected cavities and any combination thereof.

In some embodiments, solid features have a roughened surface. As usedherein, θ_(os(a)) is defined as the contact angle of oil (subscript ‘o’)on the textured solid (subscript ‘s’) in the presence of air (subscript‘a’). In certain embodiments, the roughened surface of solid featuresprovides stable impregnation of liquid therebetween or therewithin, whenθ_(os(v))>θ_(c).

In certain embodiments, liquid-impregnated surfaces described hereinhave advantageous droplet roll-off properties that minimize theaccumulation of the contacting liquid on the surfaces. Without beingbound to any particular theory, a roll-off angle α of theliquid-impregnated surface in certain embodiments is less than 50°, lessthan 40°, less than 30°, less than 25°, or less than 20°.

According to some embodiments of the present invention, an articleincludes an interior surface, which is at least partially enclosed(e.g., the article is an oil pipeline, other pipeline, consumer productcontainer, other container) and adapted for containing or transferring afluid of viscosity μ₁, wherein the interior surface comprises aliquid-impregnated surface, said liquid-impregnated surface comprisingan impregnating liquid and a matrix of solid features spacedsufficiently close to stably contain the impregnating liquidtherebetween or therewithin, wherein the impregnating liquid compriseswater (having viscosity μ₂). In certain embodiments, μ1/μ2 is greaterthan about 1, about 0.5, or about 0.1.

In certain embodiments, the impregnating liquid comprises an additive toprevent or reduce evaporation of the impregnating liquid. In someembodiments, the additive is a surfactant. Exemplary surfactantsinclude, but are not limited to, docosanoic acid, trans-13-docosenoicacid, cis-13-docosenoic acid, nonylphenoxy tri(ethyleneoxy) ethanol,methyl 12-hydroxyoctadecanate, 1-Tetracosanol, fluorochemical “L-1006”and combination thereof. More details can be found in White, Ian.“Effect of Surfactants on the Evaporation of Water Close to 100 C.”Industrial Engineering Chemistry Fundamentals 15.1 (1976): 53-59, thecontents of which are incorporated herein by references. In addition orin alternative, exemplary additives can include C₁₆H₃₃COOH, C₁₇H₃₃COOH,C₁₈H₃₃COOH, C₁₉H₃₃COOH, C₁₄H₂₉OH, C₁₆H₃₃OH, C₁₈H₃₇OH, C₂₀H_(41n)H,C₂₂H₄₅OH, C₁₇H₃₅COOCH₃, C₁₅H₃₁COOC₂H₅, C₁₆H₃₃OC₂H₄OH, C₁₈H₃₇OC₂H₄OH,C₂₀H_(41n)C₂H₄OH, C₂₂H₄₅OC₂H₄OH, Sodium docosyl sulfate, poly(vinylstearate), Poly(octadecyl acrylate), Poly(octadecyl methacrylate) andany combination thereof. More details can be found in Barnes, Geoff T.“The potential for monolayers to reduce the evaporation of water fromlarge water storages.” Agricultural Water Management 95.4 (2008):339-353, the contents of which are incorporated herein by reference.

In accordance with various embodiments, it is discovered that scaleformation may be reduced by reducing the surface energy of theunderlying liquid-impregnated surface. For example, a smooth siliconsubstrate was compared with a liquid-impregnated surface with regard tothe calcium sulfate formation thereupon. FIG. 2 includes photographs ofscale formation on these two substrates. The results demonstrate thatscale formation was significantly reduced on a liquid-impregnatedsurface, and details are described in the Experiments below.

Scale-phobic surfaces are generally described in U.S. patent applicationSer. No. 13/679,729, titled “Articles and Methods Providing Scale-PhobicSurfaces”, filed Nov. 16, 2012, the disclosure of which is herebyincorporated by reference herein in its entirety. Also, the use ofnon-wetting surfaces and, more particularly, of surfaces comprising arare-earth oxide ceramic and encapsulated with a liquid is described inU.S. patent application Ser. No. 13/741,898, filed Jan. 15, 2013, titled“Liquid-Encapsulated Rare-Earth Based Ceramic Surfaces”, the disclosureof which is hereby incorporated by reference herein in its entirety.Features of the articles and surfaces described in these patentapplications may be applied in various combinations in the variousembodiments described herein.

FIG. 1 a is a schematic cross-sectional view of a contacting liquid 102in contact with a traditional or previous non-wetting surface 104 (i.e.,a gas impregnating surface), in accordance with one embodiment of theinvention. The surface 104 includes a solid 106 having a surface texturedefined by posts 108. The regions between the posts 108 are occupied bya gas 110, such as air. As depicted, while the contacting liquid 102 isable to contact the tops of the posts 108, a gas-liquid interface 112prevents the liquid 102 from wetting the entire surface 104.

Referring to FIG. 1 b, in certain instances, the contacting liquid 102may displace the impregnating gas and become impaled within the posts108 of the solid 106. Impalement may occur, for example, when a liquiddroplet impinges the surface 104 at high velocity. When impalementoccurs, the gas occupying the regions between the posts 108 is replacedwith the contacting liquid 102, either partially or completely, and thesurface 104 may lose its non-wetting capabilities.

Referring to FIG. 1 c, in certain embodiments, a non-wetting,liquid-impregnated surface 120 is provided that includes a solid 122,e.g., a solid having textures (e.g., posts 124) that are impregnatedwith an impregnating liquid 126, rather than a gas. In the depictedembodiment, a contacting liquid 128 in contact with the surface, restson the posts 124 (or other texture) of the surface 120. In the regionsbetween the posts 124, the contacting liquid 128 is supported by theimpregnating liquid 126. In certain embodiments, the contacting liquid128 is immiscible with the impregnating liquid 126. For example, thecontacting liquid 128 may be water and the impregnating liquid 126 maybe oil.

In accordance with various embodiments, it is presently recognized thatsurface energy of a surface can be reduced by modifying a surface to beimpregnated with a liquid with a low surface energy. In someembodiments, the present invention is particularly useful for a metalsurface. The metal surface may include aluminum, steel (stainless orcarbon steel), copper, titanium, tin, or any combinations thereof.

In some embodiments, the surface includes (e.g., has a solid coatingcomprising) a fluoropolymer. The fluoropolymer may be, for example, asilsesquioxane, such as fluorodecyl polyhedral oligomericsilsesquioxane. In certain embodiments, the fluoropolymer includestetrafluoroethylene (ETFE), fluorinated ethylene-propylene copolymer(FEP), polyvinylidene fluoride (PVDF),perfluoroalkoxy-tetrafluoroethylene copolymer (PFA),polytetrafluoroethylene (PTFE), tetrafluoroethyleneperfluoromethylvinylether copolymer (MFA),ethylene-chlorotrifluoroethylene copolymer (ECTFE),ethylene-tetrafluoroethylene copolymer (ETFE), perfluoropolyether,and/or Tecnoflon, or any combination thereof.

In some embodiments, the surface includes a silane coating. In certainembodiments, the silane coating is a member selected from the groupconsisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane,fluorosilane, and any combination thereof.

The solid 122 can include the same or a different material of anunderlying layer. In some embodiments, the solid 122 may include anyintrinsically hydrophobic, oleophobic, and/or metallophobic material.For example, the solid 122 may include: hydrocarbons, such as alkanes,and fluoropolymers, such as teflon,trichloro(1H,1H,2H,2H-perfluorooctyl)silane (TCS),octadecyltrichlorosilane (OTS),heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane, fluoroPOSS,and/or other fluoropolymers. Additional possible materials or coatingsfor the solid 122 include: ceramics, polymeric materials, fluorinatedmaterials, intermetallic compounds, and composite materials. Polymericmaterials may include, for example, polytetrafluoroethylene,fluoroacrylate, fluoroeurathane, fluorosilicone, fluorosilane, modifiedcarbonate, chlorosilanes, silicone, polydimethylsiloxane (PDMS), and/orcombinations thereof. Ceramics may include, for example, titaniumcarbide, titanium nitride, chromium nitride, boron nitride, chromiumcarbide, molybdenum carbide, titanium carbonitride, electroless nickel,zirconium nitride, fluorinated silicon dioxide, titanium dioxide,tantalum oxide, tantalum nitride, diamond-like carbon, fluorinateddiamond-like carbon, and/or combinations thereof. Intermetalliccompounds may include, for example, nickel aluminide, titaniumaluminide, and/or combinations thereof.

The textures within the liquid-impregnated surface 120 are physicaltextures or surface roughness. The textures may be random, includingfractal, or patterned textures. In certain embodiments, the texturesinclude micro-scale and/or nano-scale features. For example, thetextures may have a length scale L (e.g., an average pore diameter, oran average protrusion height) that is less than about 100 microns, lessthan about 10 microns, less than about 1 micron, less than about 0.1microns, or less than about 0.01 microns. In certain embodiments, thetexture includes posts 124 or other protrusions, such as spherical orhemispherical protrusions. Rounded protrusions may be preferable toavoid sharp solid edges and minimize pinning of liquid edges. Thetexture (e.g., solid features/protrusions) may be introduced to thesurface using any conventional method, including mechanical and/orchemical methods such as lithography, self-assembly, and deposition, forexample.

The impregnating liquid 126 may be any type of liquid that is capable ofproviding the desired low surface energy. For example, the impregnatingliquid 126 may be oil-based or water-based (i.e., aqueous). In certainembodiments, the impregnating liquid 126 is an ionic liquid (e.g.,BMI-IM). Other examples of possible impregnating liquids includehexadecane, vacuum pump oils (e.g., FOMBLIN® 06/6, KRYTOX® 1506),silicone oils (e.g., 10 cSt, 50 cSt, 200 cSt, 500 cSt, or 1000 cSt, forexample), fluorocarbons (e.g., perfluoro-tripentylamine, FC-70),shear-thinning fluids, shear-thickening fluids, liquid polymers (e.g.,polyethylmethacrylate (PEMA)), dissolved polymers, viscoelastic fluids,and/or liquid fluoroPOSS. In certain embodiments, the impregnatingliquid is (or comprises) a liquid metal, a dielectric fluid, a ferrofluid, a magneto-rheological (MR) fluid, an electro-rheological (ER)fluid, an ionic fluid, a hydrocarbon liquid, and/or a fluorocarbonliquid, or any combination thereof.

The impregnating liquid 126 may be introduced to the surface 120 usingany conventional technique for applying a liquid to a solid. In certainembodiments, a coating process, such as a dip coating, blade coating, orroller coating, is used to apply the impregnating liquid 126.Alternatively, the impregnating liquid 126 may be introduced and/orreplenished by liquid materials flowing past the surface 120 (e.g., in apipeline). After the impregnating liquid 126 has been applied, capillaryforces stably hold the liquid in place. Capillary forces scale roughlywith the inverse of feature-to-feature distance or pore radius, and thefeatures may be designed such that the liquid is held in place despitemovement of the surface and despite movement of air or other fluids overthe surface (e.g., where the surface 120 is on the outer surface of anaircraft with air rushing over, or in a pipeline with oil and/or otherfluids flowing therethrough). In certain embodiments, nano-scalefeatures are used (e.g., 1 nanometer to 1 micrometer) where high dynamicforces, body forces, gravitational forces, and/or shearing forces couldpose a threat to remove the liquid film, e.g., for surfaces used in fastflowing pipelines.

In some embodiments, a liquid-impregnated surface is configured suchthat the impregnating liquid submerges a portion of, or the entire,surface with solid features thereupon. As used herein, emerged areafraction φ is defined as a representative fraction of the projectedsurface area of the liquid-impregnated surface corresponding tonon-submerged solid at equilibrium. The term “equilibrium” as usedherein refers to the condition in which the average thickness of theimpregnating film does not change over time due to drainage by gravitywhen the substrate is held away from horizontal, and where evaporationis negligible (e.g., if the liquid impregnated liquid were to be placedin an environment saturated with the vapor of that impregnated liquid).Similarly, the term “pseudo-equilibrium” as used herein refers to thesame condition except that evaporation may occur, or gradual dissolving.In certain embodiments, equilibrium is a relative term—e.g., someevaporation or gradual dissolving of impregnating liquid may beoccurring, but the article is still considered to be “at equilibrium”.Note that the average thickness of a film at equilibrium may be less onparts of the substrate that are at a higher elevation, due to thedecreased hydrostatic pressure within the film at increasing elevation.However, it will eventually reach an equilibrium or pseudo-equilibrium,in which the average thickness of any part of the surfaces is unchangingwith time.

In general, a “representative fraction” of a surface refers to a portionof the surface with a sufficient number of solid features thereupon suchthat the portion is reasonably representative of the whole surface. Incertain embodiments, a “representative fraction” is at least a tenth ofthe whole surface.

Referring to FIG. 3, a schematic cross-sectional view and thecorresponding top view of a liquid-impregnated surface that is partiallysubmerged is shown. The upper left drawing of FIG. 3 shows across-sectional view of a row of cone-shaped solid features. Theprojected surface area of the non-submerged solid 302 is illustrated asshaded areas of the overhead view, while the remaining non-shaded arearepresents the projected surface area of the submergedliquid-impregnated surface 300. In addition to the projection surfacearea of this row of solid features, other solid features placed in asemi-random pattern are shown in shade in the overhead view. Similarly,the cross-section view of a row of evenly spaced posts is shown on theright of FIG. 3. Additional rows of well-patterned posts are shown inshade in the overhead view. As demonstrated, in some embodiments of thepresent invention, a liquid-impregnated surface includes randomly and/ornon-randomly patterned solid features.

In some embodiments discussed herein, a novel approach for impartingand/or improving scale-resistance using lubricant-impregnated surfacesin which a liquid lubricant is impregnated into a micro/nanotexturedsurface is illustrated. FIG. 10 b shows such a lubricant-impregnatedsurface. The impregnated lubricant is stabilized by capillary forcesarising from the microscopic texture and can impart remarkable mobilityto droplets (or other motive phases) on the surface, provided thelubricant preferentially spreads on the solid. These types of surfaceshave been shown to repel a variety of liquids, enhance condensation,reduce ice adhesion, and exhibit self-cleaning, among other propertiesand advantages. High capillary stabilization and self-healing propertiesmake these surfaces robust enough to withstand harsh conditions, such asthose in, e.g., oil pipelines or heat exchangers.

Some embodiments discussed herein relate to the control of gypsum scaledeposition on surfaces exposed to supersaturated saline solutions. Anuntreated smooth surface experiences heavy scale deposition with a veryhigh surface coverage (as seen in FIGS. 10 c and 10 e). In contrast, alubricant-impregnated surface shows almost negligible scale depositioncompared to an untreated surface, as shown in FIG. 10 d. Thecorresponding SEM image of the lubricant-impregnated surface (shown inFIG. 10 f) further shows almost negligible surface coverage of scale onthe lubricant-impregnated surface. This remarkable performance of thelubricant-impregnated surface is a result of the texture and theimpregnating lubricant (e.g., the choice of the lubricant, the amount ofthe lubricant, the manner of deposition of the lubricant, the combinedproperties of the lubricant/impregnating surface, etc.).

In certain embodiments, an apparatus or device (e.g., a vessel, such asa conduit, receptacle, pipeline, or the like) is provided that reducesor prevents the formation of mineral scale. The mineral scale mayinclude, for example, calcium sulfate, calcium carbonate, bariumsulfate, silica, iron, and/or other deposits and any combinationthereof. In certain embodiments, the device reduces or prevents theformation of mineral scale by having a surface with a low surfaceenergy, said surface having exposure to a mineral solution.

In certain embodiments, a method of retrofitting a device (e.g., avessel) is provided for improved resistance to scale formation. Themethod may include modifying a surface of the device with aliquid-impregnated surface in accordance with the present invention.

In some embodiments, the invention relates to an article for use inindustrial operation or research set-ups, the article having a surfacewith lowered surface energy. In certain embodiments, the article is apipeline (or a part or coating thereof), and the surface is configuredto inhibit scale formation thereupon. In certain embodiments, thearticle is a heat exchanger part or an oil or gas pipeline (or a part orcoating thereof), and the surface is configured to inhibit scaleformation thereupon.

EXPERIMENTAL EXAMPLES Example 1

In this example, scaling experiments were conducted using calciumsulfate solution at a temperature of about 45° C. Bare smooth silicon,silanized silicon, silicon nanograss, silanized nanograss, and liquidimpregnated surfaces were tested.

To systematically study scale formation on the test substrates, thesesubstrates were immersed inside a 600 ml glass beaker. To reduce thesurface energy of the dish and slides rack and prevent preferentialscale formation, the substrates were coated withtrichloro(1H,1H,2H,2H-perfluorooctyl)silane before the experiment. Theglass beaker was filled with a saturated solution of CaSO₄ in water andplaced on a multi-position hotplate (Ika Works IKAMAG RT 15 position HotPlate). Temperature was set at 45° C. and controlled within ±3° C. ofthe set point. The experimental set-up allows the solutions to reachsupersaturation through evaporation of the aqueous phase during thecourse of experiment (80 h).

FIG. 4 shows a schematic illustration of the experimental set-up.Containers were made of glass and were coated with a low surface energymodifier (here, we used fluorosilane) to inhibit preferential nucleationof the salts.

The substrate samples were withdrawn at three time intervals (i.e., 33,53, 80 h). The withdrawn substrate samples were air-dried and weightedusing a high accuracy balance to quantify their weight change due to thedeposition of CaSO₄ precipitates on their surfaces. To study their scaledeposition qualitatively, substrate samples were also characterizedusing SEM (JSM-6610LV) at an accelerating voltage of 20 kV.

The nanograss was grown on smooth silicon substrates by dry etching,where the substrate was placed inside an inductively coupled plasmachamber with a controlled flow of etching gases (SF₆/O₂) for ˜10 min.The average width of the grass wires was ˜100 nm with spacing of˜100-200 nm. Before liquid impregnation, the nanograss covered siliconwas modified with OTS (octadecyltricholrosilane).

To fabricate the oil-encapsulated surface, the OTS coated nanograsssamples were dip-coated in silicone oil (100 cSt), using a dip-coater(KSV Nima multi-vessel dip-coater). The dip-coated surfaces wereretracted at a predetermined speed such that the capillary number waswell below 10⁻⁵. This enabled the nanostructure to be effectivelyimpregnated with the liquid.

Octadecyltricholrosilane (OTS) (90%) was purchased from Sigma Aldrich.Polyethylmethacrylate (PEMA) was purchased from Sigma Aldrich and wasdissolved in Asahiklin—an organic solvent. Calcium sulfate dihydrate(99.4%) was purchased from J.T. Baker and dissolved directly indeionized water (18 MΩ-cm, Millipore) to make the starting saturatedsolution. Silicone oil (100 cSt) was purchased from Sigma Aldrich.

A smooth silicon surface was textured with nano-features (nanograss)using reactive ion etching and the surface was then coated withoctadecyltrichlorosilane (OTS) to lower its surface energy as discussedabove. The nanograss substrates were then impregnated with twolubricants—Silicone oil (Sigma Aldrich—polydimethylsiloxane, surfacetension at 25° C. is 20 mN/m), having a positive spreading coefficienton OTS and DC704 (Dow Corning—tetramethyl tetraphenyl trisiloxane,surface tension at 25° C. is 37.3 mN/m), having a negative spreadingcoefficient on OTS. Table 1 below shows the contact angles of the twolubricants on OTS, which are less than the critical contact angle Θ_(c),resulting in stable impregnated states (Θ_(c)˜78° on nanograss). Becausesilicone oil has a low surface tension and a positive spreadingcoefficient, the resulting impregnated surface is in the most preferredstate (state IV in FIG. 1 d) for scale inhibition. In contrast, DC704has a negative spreading coefficient and a higher surface tension,resulting in a state that is more susceptible to scale formation (stateI in FIG. 1 d).

TABLE 1 Contact angle data for the lubricants on an OTS-treated smoothsurface. Lubricant Advancing (°) Receding (°) Silicone Oil 0 0 DC704 55± 1 42 ± 2

Scaling phenomenon was observed on surfaces with different impregnatingliquids—silicone oil and a diffusion pump liquid (DC704). Silicone oilsubmerges the entire texture resulting in an extremely smooth surfacewith no exposed texture. Additionally, the impregnating liquid is a lowsurface tension liquid, and the amount of scale formed on this surfaceis observed to be very low (see FIG. 5 a). In contrast, DC704 being ahigh surface tension liquid results in higher energy surface with theliquid that does not completely submerge the texture thus resulting inincreased scaling compared to the silicone oil case (see FIG. 5 b).

FIG. 6 includes two graphs showing mass gain due to scale formation onvarious substrates; the results are expressed as a fraction of the massgain observed on uncoated smooth silicon. The scale depositionexperiment was conducted on uncoated and silanized smooth silicon,uncoated and silanized nano-textured silicon, DC704-impregnated, andsilicone oil-impregnated nano-textured silicon. Because of its lowsurface energy and limited density of nucleation sites, the resultsobtained with the silicone oil-impregnated surface were at least 10times better than the uncoated smooth silicon substrate and uncoatednanograss silicon substrate in resisting scale formation. The siliconeoil-impregnated surfaces had lesser scale formation than thesilane-coated nanograss substrate, which is thought to be due to theincreased roughness (higher density of nucleation sites) of thesilanized nanograss silicon substrate. The performance ofDC704-impregnated surface in resisting scale formation was worse thanthat of the silicone oil-impregnated surface. This is thought to be dueto the presence of a high surface tension lubricant and higher densityof nucleation sites, which is consistent with the results illustrated inFIG. 1 d. The mass gain was due to calcium sulfate formation on thesurfaces after being immersed in the salt solution for ˜80 hours,expressed as a normalized parameter with respect to silicon.

There was a significant reduction in the amount of scale formed on theliquid impregnated surfaces compared to the case of smooth silicon andrough silicon nanograss both in terms of mass gain and surface coverage.More specifically, the silicone oil-impregnated sample shows a betterperformance in comparison to the silanized smooth silicon samples. Thedata confirms that an impregnating liquid whose surface tension/surfaceenergy density is below that of ˜20-25 mJ/m² (e.g., OTS-silane), providea better anti-scaling performance than the silanized smooth surface.

Along with a reduction in the total amount of scale formed, there isalso a delay in the nucleation of the salt particles on the liquidimpregnated surfaces compared to the bare smooth surface.

Calcium sulfate dihydrate (gypsum) was used in the experiments below tostudy scale deposition. The test substrates were immersed in a saturatedsolution of calcium sulfate dihydrate, and the entire system wasmaintained at an elevated temperature (see FIG. 7 a). Thesupersaturation required for the nucleation of salt was achieved by theevaporation of the solution. The surface coverage of the scale depositedon an uncoated smooth silicon substrate was compared to that on asilicone oil-impregnated nano-textured silicon substrate sampled atthree different times (33, 53 and 80 hours) during the experiment (seeFIGS. 7 c and 7 d). The lower amount of scale formed on thelubricant-impregnated surface is thought to be due to the reducednucleation rate. While nucleation had begun at ˜33 hours on smoothsilicon (FIG. 7 c), little to no nucleation was observed on the siliconeoil-impregnated surface even after 53 hours (FIG. 7 d). Thecorresponding surface coverage on the two surfaces at different times isshown in FIG. 7 b (Image analysis done using ImageJ).

As illustrated by these images, the surface coverage is negligible onthe silicone oil-impregnated surface compared to the uncoated smoothsilicon, consistent with the nucleation theory presented herein. Thereduced nucleation rate on silicone oil-impregnated surface is likelydue to the low density of nucleation sites and a high activation barrierfor nucleation (low-energy surface).

Example 2

In this Example, scaling experiments were conducted on stainless steeland carbon steel. Carbon steel is a low cost structural material whoselow corrosion resistance is a serious drawback in certain industrialapplications. This example demonstrates that by texturing andliquid-impregnating stainless steel and carbon steel surfaces, suchsurfaces can be made to become more resistant to scale formation.

The experimental setup was similar to the one described for siliconsubstrates in Example 1.

Stainless-steel (type 304, ASTM A240, from Mcmaster) and carbon-steel(grade 1010, ASTM A109, also from Mcmaster) were sand-blasted usingsilica and alumina particles of 80 grit size for ˜3 min. The featuresize of the sandblasted steel is roughly 10 μm. In certain embodiments,the feature size for liquid impregnation may be less than about 100 μm.

After sand-blasting, polyethylmethacrylate (PEMA) (surface energydensity 33 J/m²) was used to modify the surface energy of steelsubstrates. The textured steel substrate was coated with PEMA to lowerits surface energy and achieve a stable impregnation by silicone oil.PEMA dissolved in Asahiklin was applied on the steel substrates via spincoating with the substrate rotated at a speed of 1000 rpm.

In addition to a schematic of liquid impregnation in steel, FIG. 8 showsan SEM image of sand-blasted stainless steel before impregnation withsilicone oil (scale bar 50 μm). Also shown are photographs of barestainless steel before washing (c) and after washing (d); photographs ofthe liquid-impregnated stainless steel before washing (g) and afterwashing (h). The corresponding SEM images of both bare steel ((e) and(f)) and the liquid-impregnated stainless steel ((i) and (j)) are shownas well. The adhesion of the salt particles to the liquid impregnatedsurface was observed to be extremely low compared to the bare stainlesssteel substrate, which indicates that the scale formed can easily bewashed into the bulk.

The liquid within the textures lasted throughout the experiment (˜80hours), and hence provides an indication of its longevity in theseapplications.

A decrease in the amount of scale formed on the lubricant-impregnatedsteel compared to an uncoated smooth steel surface was observed (asshown in FIGS. 8 c, 8 d). The two substrates were washed with a steadystream of water at a flow rate of ˜150 ml/min for ˜30 seconds. Afterwashing, the lubricant-impregnated steel appeared scale-free (FIG. 8 h),while the smooth uncoated stainless steel had significant depositsremaining on the surface (as seen in FIG. 8 g). Thus, texturingtechniques such as sandblasting assist in reducing scale deposition andalso help lower the adhesion of scale to lubricant-impregnated surfaces.

In some embodiments, lubricant-impregnated surfaces with low orextremely low evaporation rates are used to prevent depletion of thelubricant. In some embodiments, the set-ups discussed above may beconnected to a replenishing reservoir to replenish the lubricant if itbecomes depleted or if the level of the lubricant falls below apredetermined threshold (or e.g., may be replenished periodically).

The liquid-impregnated carbon steel not only shows a decrease in theamount of scale formed on the surfaces, but it also provides bettercorrosion resistance, as shown in FIG. 9), making it very attractive instructural applications.

EQUIVALENTS

While the invention has been particularly shown and described withreference to specific preferred embodiments, it should be understood bythose skilled in the art that various changes in form and detail may bemade therein without departing from the spirit and scope of theinvention as defined by the appended claims.

What is claimed is:
 1. A vessel for use in an industrial process, thevessel comprising a liquid-impregnated interior surface, wherein theliquid-impregnated surface comprises a matrix of features spacedsufficiently close to stably contain an impregnating liquid therebetweenor therewithin and the impregnating liquid has a surface energy densityγ (as measured at 25° C.) no greater than about 35 mJ/m², therebyproviding resistance to mineral scale deposits thereupon.
 2. The vesselof claim 1, wherein the liquid-impregnated surface comprises the matrixof features spaced sufficiently close to contain the impregnating liquidsufficiently well such that small quantities of impregnating liquid lostdue to settling, evaporation, and/or dissolution of the impregnatingliquid into one or more phases coming into contact with the surface canbe replenished.
 3. (canceled)
 4. The vessel of claim 1, wherein thesurface energy density γ (as measured at 25° C.) is no greater thanabout 30 mJ/m², no greater than about 25 mJ/m², or no greater than about20 mJ/m². 5.-6. (canceled)
 7. The vessel of claim 1, wherein theimpregnating liquid is immiscible with, or negligibly miscible with, thesolution comprising the scale-forming mineral with which the interiorsurface of the vessel is designed to come into contact.
 8. The vessel ofclaim 1, wherein the impregnating liquid is a lubricant and the interiorsurface is a textured substrate, wherein the liquid-impregnated interiorsurface of the vessel is configured, during operation, to come intocontact with (or maintain contact with) a salt solution comprising ascale-forming mineral, and wherein the spreading coefficient S_(os(w))of the impregnating lubricant (subscript ‘o’) on the substrate(subscript ‘s’) in the presence of the salt solution (subscript ‘w’) isgreater than zero, such that the impregnating lubricant fully submergesthe textured substrate.
 9. The vessel of claim 1, wherein the vessel isdesigned for use in a process in which the liquid-impregnated surface ofthe vessel is in contact with a salt solution comprising a scale-formingmineral, or wherein the vessel contains a salt solution comprising ascale-forming mineral or transfers a salt solution comprising ascale-forming mineral.
 10. The vessel of claim 1, wherein theimpregnating liquid is a silicone oil.
 11. The vessel of claim 1,wherein the liquid-impregnated surface is a scale-phobic surface thatinhibits scale formation thereupon.
 12. The vessel of claim 1, whereinthe liquid-impregnated surface comprises a (solid) metal or wherein theliquid-impregnated surface comprises a metal selected from the groupconsisting of aluminum, steel, copper, titanium, tin, or any combinationthereof. 13.-14. (canceled)
 15. The vessel of claim 1, wherein theliquid-impregnated surface comprises a silane coating.
 16. The vessel ofclaim 15, wherein the silane coating is a member selected from the groupconsisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane, andfluorosilane.
 17. The vessel of claim 1, wherein the liquid-impregnatedsurface is textured.
 18. The vessel of claim 1, wherein theliquid-impregnated surface comprises micro-scale and/or nano-scalefeatures and/or wherein the features comprise nanograss.
 19. (canceled)20. The vessel of claim 1, wherein the liquid-impregnated surface islocated on an interior wall of a heat exchanger.
 21. The vessel of claim1, wherein the mineral scale deposits comprise at least one of calciumsulfate, calcium carbonate, barium sulfate, silica, and/or iron.
 22. Thevessel of claim 1, wherein the vessel is a conduit or receptacle used indeep sea oil and/or gas recovery or wherein the vessel is a conduit orreceptacle of a heat exchanger.
 23. (canceled)
 24. A method ofretrofitting a vessel for improved resistance to mineral scale deposits,the method comprising modifying the vessel to produce aliquid-impregnated surface, wherein the liquid-impregnated surfacecomprises a matrix of features spaced sufficiently close to stablycontain an impregnating liquid therebetween or therewithin and theimpregnating liquid has a surface energy density γ (as measured at 25°C.) no greater than about 35 mJ/m², thereby providing resistance tomineral scale deposits thereupon.
 25. The method of claim 24, whereinthe liquid-impregnated surface comprises the matrix of features spacedsufficiently close to contain the impregnating liquid sufficiently wellsuch that small quantities of impregnating liquid lost due to settling,evaporation, and/or dissolution of the impregnating liquid into one ormore phases coming into contact with the surface can be replenished.26.-27. (canceled)
 28. The method of claim 24, wherein the impregnatingliquid is a lubricant and the interior surface is a textured substrate,wherein the liquid-impregnated interior surface of the vessel isconfigured, during operation, to come into contact with (or maintaincontact with) a salt solution comprising a scale-forming mineral, andwherein the spreading coefficient S_(os(w)) of the impregnatinglubricant (subscript ‘o’) on the substrate (subscript ‘s’) in thepresence of the salt solution (subscript ‘w’) is greater than zero, suchthat the impregnating lubricant fully submerges the textured substrate.29. The method of claim 28, wherein the vessel is designed for use in aprocess in which the liquid-impregnated surface of the vessel is incontact with a salt solution comprising a scale-forming mineral, orwherein the vessel contains a salt solution comprising a scale-formingmineral or transfers a salt solution comprising a scale-forming mineral.30. The vessel of claim 24, wherein the impregnating liquid isimmiscible with, or negligibly miscible with, the solution comprisingthe scale-forming mineral with which the interior surface of the vesselis designed to come into contact.
 31. The method of claim 24, whereinthe impregnating liquid is a silicone oil. 32.-35. (canceled)
 36. Themethod of claim 24, wherein the liquid-impregnated surface comprises asilane coating, wherein the silane coating is a member selected from thegroup consisting of methylsilane, phenylsilane, isobutylsilane,dimethylsilane, tetramethyldisilane, hexylsilane, octadecylsilane, andfluorosilane. 37.-38. (canceled)
 39. The method of any one of claim 24,wherein the liquid-impregnated surface comprises micro-scale and/ornano-scale features. 40.-44. (canceled)
 45. A method of using a vesselin an industrial process, the method comprising: (a) providing a vesselcomprising a liquid-impregnated surface, wherein the liquid-impregnatedsurface comprises a matrix of features spaced sufficiently close tostably contain an impregnating liquid therebetween or and theimpregnating liquid has a surface energy density γ (as measured at 25°C.) no greater than about 35 mJ/m², thereby providing resistance tomineral scale deposits thereupon; and (b) contacting theliquid-impregnated surface with a solution comprising a scale-formingmineral.
 46. The method of claim 45, wherein the impregnating liquid isimmiscible with, or negligibly miscible with, the solution comprisingthe scale forming mineral with which the interior surface of the vesselis designed to come into contact.
 47. The method of claim 45, furthercomprising contacting the liquid-impregnated surface with a reservoircontaining the impregnating liquid to replenish any impregnating liquidlost due to settling, evaporation, and/or dissolution into one or moreother phases coming into contact with the liquid-impregnated surface.48. The method of claim 45, wherein the impregnating liquid is alubricant and the interior surface is a textured substrate, wherein theliquid-impregnated interior surface of the vessel is configured, duringoperation, to come into contact with (or maintain contact with) a saltsolution comprising a scale-forming mineral (e.g., wherein the vessel isdesigned for use in a process in which the liquid-impregnated surface ofthe vessel is in contact with a salt solution comprising a scale-formingmineral, or wherein the vessel contains a salt solution comprising ascale-forming mineral or transfers a salt solution comprising ascale-forming mineral), and wherein the spreading coefficient S_(os(w))of the impregnating lubricant (subscript ‘o’) on the substrate(subscript ‘s’) in the presence of the salt solution (subscript ‘w’) isgreater than zero, such that the impregnating lubricant fully submergesthe textured substrate.
 49. The method of claim 45, wherein theimpregnating liquid is a silicone oil.
 50. The method of claim 45,wherein the liquid-impregnated surface is a scale-phobic surface thatinhibits scale formation thereupon. 51.-53. (canceled)
 54. The method ofclaim 45, wherein the liquid-impregnated surface comprises a silanecoating. 55.-56. (canceled)
 57. The method of claim 45, wherein theliquid-impregnated surface comprises micro-scale and/or nano-scalefeatures and/or nanograss. 58.-64. (canceled)